(e,e'pp) and (e,e'pn) and the role of...
TRANSCRIPT
L. Weinstein, Gordon 2004 1
(e,e'pp) and (e,e'pn) and the role of correlations
Lawrence Weinstein Old Dominion University
• Nucleons One by One • What are Correlations? • How big are they? • np vs pp pairs • Summary
Neutrino Interactions in Nuclei, 2014
Fermi gas model: how simple a model can you make ?
e
e’
pf
q pi Initial nucleon energy:
Final nucleon energy:
Energy transfer:
KEi= pi2 /2mKEf =(
!q+ !pi)2 /2mν =KEf −KEi=q
2 /2m+(!q⋅ !pi)/m
!Peak Centroid:
Width: Cross section:
ν = !q2 /2mΔν =(!q⋅ !pi)/mσ total=Zσep+Nσen
R.R. Whitney et al., PRC 9, 2230 (1974).
C(e,e’)
0.10 0.30 ν [GeV]
Cro
ss se
ctio
n [n
b/sr
-GeV
]
Fermi gas model
0.20
Virtual photon: Momentum q, energy ν Q2=qµqµ =|
!q |2−ν2>0
e
e’
pf q pi
Get more information: detect a knocked out nucleon (e,e’p)
Missing energy: Missing momentum:
Emiss=ν−T ′p −TA−1!pmiss=!q− !pf
Proton rescattering ! Distorted spectral fn
!pi ≈−!pmiss
No proton rescattering !
!pi=−!pmiss
dσdνdΩedEmissdΩp
=KS(pi,Emiss)dσepdΩ
Spectral fn S = probability of finding a proton with momentum pi and binding energy Emiss
O(e,e’p) shells p1/2 p3/2
s1/2
1p1/2, 1p3/2 and 1s1/2 shells visible
Momentum distribution as expected for L = 0, 1
p1/2
p3/2
Fissum et al, PRC 70, 034606 (2003)
Pmiss -300 300
p1/2
p3/2
!High momentum tails: k > kF Calculable for A ≤ 12 nuclei and nuclear matter. Not well constrained at k >> kf
Deuteron
Carbon
NM
7
Short Range Correlations (SRCs)
Nucleons are like people …
k > 250 MeV/c 25% of nucleons 60% of KE
k < 250 MeV/c 75% of nucleons 40% of KE
p (GeV/c)
n(p)
(GeV
/c)-3
0.8 0.2
1.7 fm ~1.0 fm
ρ0 = 0.16 fm-3
2N-SRC ρ ~ 5ρ0
Effects: • High momentum part of the nuclear wave function • Short distance behavior of nucleons - modification?? • Cold dense nuclear matter • Neutron Stars
Correlations and High Momentum
Momentum (1/fm) Momentum (1/fm) Ciofi degli Atti, PRC 53 (1996) 1689
Correlations p-15N breakup
Continuum Continuum
p-d breakup Corr M
omen
tum
Den
sity
Average Two-Nucleon Properties in the Nuclear Ground State Responsible for the high momentum part of of the Nuclear WF
Two-body currents are not Correlations (but add coherently)
What are correlations?
!
!
in SRC
Signatures for Correlations
An Experimentalist’s Definition: • A high momentum nucleon whose
momentum is balanced by one other nucleon • NN Pair with
• Large Relative Momentum • Small Total Momentum
Correlations are Universal: A(e,e’)
N. Fomin et al, PRL 108, 092502 (2012) α2N ≈20%
Scaling (flat ratios) indicates a common momentum distribution. 1 < x < 1.5: dominated by different mean field n(k) 1.5 < x < 2: dominated by 2N SRC
Cro
ss se
ctio
n ra
tio to
deu
teriu
m
x=Q2 /2mν
Q2 = 2.5 GeV2
EMC dREMC/dx
SRC a2N
1 1.5 0.5
SRC and the EMC Effect
xB
EMC effect and SRC are both due to high momentum nucleons " nucleon modification due to
nucleon motion?
PRL 106, 052301 (2011)
EMC effect: reduction of the per-nucleon DIS cross section relative to deuterium at 0.3 < xB < 0.7 • Implies nucleon modification
12C(p,ppn) EVA/BNL
cosγ
Large neutron momentum n opposite pinit
Small neutron momentum n isotropic
High momentum nucleons are paired Tang et al, PRL 90, 042301 (2003)
p
p p
n
12C γ
Pmiss = 300, 400, 500 MeV/c
e
e’
*γn or p p
P =
300-
600
MeV
/c
Ee = 4.627 GeV
Ee’ = 3.724 GeV
50.40
19.50
40.1, 35.8, 32.00
Now detect yet another nucleon JLab Hall A C(e,e’pN) - selected kinematics
Q2 = 2 GeV2
xB = Q2/2mν = 1.2 Pmiss = 300-600 MeV/c
Detect the proton, look for its partner nucleon
Missing Momentum [GeV/c]
0.3 0.4 0.5 0.6
SR
C P
air
Fracti
on
(%
)
10
210
C(e,e’p) ] /212
C(e,e’pp) /12
pp/2N from [
C(e,e’p)12
C(e,e’pn) /12
np/2N from
C(p,2p)12
C(p,2pn) /12
np/2N from
C(e,e’pn) ] /212
C(e,e’pp) /12
pp/np from [
High momentum protons have partners C(e,e’pN)
• Detect the knocked-out proton
• Look for its partner nucleon
• All high momentum protons have partners
!np pairs dominate at 0.3<pi<0.6
pp pairs
np pairs
R. Subedi et al., Science 320, 1476 (2008)
Higher momentum protons? 4He(e,e’pN)
• pp pairs still only 5% of high momentum protons • np pairs decrease with missing momentum • Three nucleon correlations???
I. Korover et al., arXiv:1401.6138
SRC
Fra
ctio
n [%
] .
.
5
100
40
10
pn/p
pp/p
pp/pn
The ratio of pp-SRC / pn-SRC pairs in 12C
Why ?
There are 18 ± 2 times more np-SRC than pp-SRC pairs in 12C.
At prel = 300-500 MeV/c the s-wave momentum distribution has a minimum The np minimum is filled in by strong tensor correlations
Schiavilla, Wiringa, Pieper, Carlson, PRL 98, 132501 (2007).
Sargsian, Abrahamyan, Strikman, Frankfurt PRC 71, 044615 (2005).
3He
V18
np
pp
Ciofi and Alvioli Gent workshop, Aug. 2007
Pair relative momentum
pn
pp
3He 8Be
Pair relative momentum
Pair relative momentum
4He
3He(e,eX) in JLab CLAS
2.2 and 4.7 GeV electrons Inclusive trigger Almost 4π detector
TOF CER CAL
DC1 DC2
DC3
CLAS
3He(e,e’pp)
Detect 2 protons, reconstruct the neutron
Huge electron acceptance
<Q2> ~ 0.8
<Q2> ~ 1.8
3He(e,e’pp)n nucleon energy balance
Select peaks in Dalitz plot
Pair has back-to-back peak!
pn pair
pp
Similar momentum distributions • Relative • Total
pn / pp ratio ~ 4
Results:
Q2≈0.8 GeV2 reduced by 5.3
cros
s se
ctio
n (f
b/M
eV)
5
10
15
20
pn pair
a)
pn pair
b)
(GeV/c)relp0 0.2 0.4 0.6
cros
s se
ctio
n (f
b/M
eV)
1
2
3
4
pp pairc)
(GeV/c)totp0 0.2 0.4 0.6
pp paird)
0.8 GeV2 1.5 GeV2
pn pair
pp pair pp pair
pn pair
pp to pn comparison
Ebeam <Q2> pn to pp ratio
Hall A / BNL
2 / ?? 18
Hall B 0.8 – 1.5 4
Contradiction???
Subedi et al, Science (2008)
Relative
np/2N
pp/2N
12C
BNL Hall A
HALL A Hall A
pp to pn resolution: pp/pn ratio increases with pair total momentum Ptot
Hall A: small Ptot ! less pp Hall B: large Ptot ! more pp
Small Ptot ! pp pair in s-wave (no tensor) ! wave fn minimum at prel=400 MeV/c
300 < Prelative < 500 MeV/c Tensor Correlations!
Hall A / BNL
Golak 1-body
3He mom dist
data
PRL 105, 222501 (2010)